ematical models to explain them. Among the organizations tuned into this issue is Microsoft, which obviously has a great interest in the Internet and World Wide Web. So their top scientists are busy investigating network math themselves. Leaders of this pack are a husband-wife team, mathematician Jennifer Tour Chayes and her husband/collaborator Christian Borgs. When I visited the Microsoft research labs outside Seattle, they outlined to me their efforts to identify the features that network math needs in order to capture the essence of the Web’s structure.

“The Internet and the World Wide Web are grown, they’re not engineered,” Chayes pointed out. “No one really planned the Internet, and certainly no one planned the structure of the World Wide Web.” Consequently the Web embodies many of the nuances of natural networks that a good mathematical model will need to capture, such as the small-world property (the ability to get from one page to any other in a relatively few number of steps) and the clustering phenomenon (if a Web page links to 10 others, there’s a good chance that many of those 10 will link to one another as well). A further important feature is the preferential attachment identified by Barabási that conditions how a network grows, or ages. As the Web grows, and pages are added to the network, the older pages do tend to acquire more links than newcomers. But it’s not always true that the oldest pages are the most connected. “It’s not just a function of aging,” Chayes explained. AltaVista, for example, once was the Cadillac of Web search engines. But the younger Google now has many more links. So different sites must earn links not only by virtue of age, but also beauty—or “fitness.”

“AltaVista has been around longer but more people tend to link to Google—it’s in some sense a better page,” said Chayes. “All other things equal, the older sites will on average have more links, but if one site is more fit than another, that compensates for age…. If I’m twice as fit and I’m half as old, I should tend to have about the same number of connections.”9

Another important feature of the Web, shared by many (but not all) networks, is that the links are “directed.” Unlike the Internet, where wires run both ways, Web page hyperlinks go in only one



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